%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP388-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:37 PM UTC 2026
% Result : Unsatisfiable 4.57s 2.09s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 229 ( 71 unt; 13 def)
% Number of atoms : 793 ( 457 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 409 ( 148 ~; 261 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
inverse(sk_c10) = sk_c9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f10]) ).
fof(f18,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c9 = multiply(sk_c10,sk_c2) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c2) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = multiply(sk_c10,sk_c2) ),
inference(reorient_equations,[],[f26]) ).
fof(f38,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c2 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c2 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c10 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f42]) ).
fof(f52,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c6 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c8 = multiply(sk_c6,sk_c9)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c10 != multiply(X6,sk_c8)
| sk_c10 != inverse(X6)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5
| sk_c8 != multiply(X4,X5)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2
| sk_c9 != multiply(sk_c10,X2)
| sk_c10 != inverse(X1)
| multiply(X1,sk_c10) != X0
| sk_c9 != multiply(sk_c10,X0)
| sk_c10 != multiply(sk_c8,sk_c9)
| inverse(sk_c10) != sk_c9 ),
inference(reorient_equations,[],[f70]) ).
fof(f72,plain,
! [X2,X3,X1,X6,X4,X5] :
( sk_c10 != multiply(X6,sk_c8)
| sk_c10 != inverse(X6)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5
| sk_c8 != multiply(X4,X5)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2
| sk_c9 != multiply(sk_c10,X2)
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != multiply(sk_c8,sk_c9)
| inverse(sk_c10) != sk_c9 ),
inference(equality_resolution,[],[f71]) ).
fof(f73,plain,
! [X3,X1,X6,X4,X5] :
( sk_c10 != multiply(X6,sk_c8)
| sk_c10 != inverse(X6)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5
| sk_c8 != multiply(X4,X5)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != multiply(sk_c8,sk_c9)
| inverse(sk_c10) != sk_c9 ),
inference(equality_resolution,[],[f72]) ).
fof(f74,plain,
! [X3,X1,X6,X4] :
( sk_c10 != multiply(X6,sk_c8)
| sk_c10 != inverse(X6)
| sk_c8 != multiply(inverse(X4),sk_c9)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != multiply(sk_c8,sk_c9)
| inverse(sk_c10) != sk_c9 ),
inference(equality_resolution,[],[f73]) ).
tcf(c_86,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_87,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_89,negated_conjecture,
inverse(sk_c10) = sk_c9,
inference(cnf_transformation,[],[f5]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c8,sk_c9) = sk_c10 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c3,sk_c10) = sk_c4 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_97,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c10 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c10,sk_c2) = sk_c9 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c3,sk_c10) = sk_c4 )
| ( multiply(sk_c10,sk_c2) = sk_c9 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c10,sk_c2) = sk_c9 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c2 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c2 )
| ( multiply(sk_c3,sk_c10) = sk_c4 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c1,sk_c10) = sk_c2 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c2 )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c3,sk_c10) = sk_c4 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c3) = sk_c10 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c6,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_122,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c10) != sk_c9 )
| ( inverse(X2) != sk_c10 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c8,sk_c9) != sk_c10 )
| ( multiply(X0,sk_c8) != sk_c10 )
| ( multiply(inverse(X3),sk_c9) != sk_c8 )
| ( multiply(X3,inverse(X3)) != sk_c8 )
| ( multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9 )
| ( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 )
| ( multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9 )
| ( multiply(X3,inverse(X3)) != sk_c8 )
| ( multiply(inverse(X3),sk_c9) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c10 )
| ( multiply(sk_c8,sk_c9) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X2) != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_122,c_89,c_122]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c10 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c8,sk_c9) != sk_c10 )
| ( multiply(X3,sk_c8) != sk_c10 )
| ( multiply(inverse(X2),sk_c9) != sk_c8 )
| ( multiply(X2,inverse(X2)) != sk_c8 )
| ( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(renaming,[status(thm)],[c_127]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c9) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_433,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_434,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c8) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_435,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c8,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_436,definition,
iPr_def_13 = multiply(sk_c8,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_437,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_438,definition,
iPr_def_15 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_439,definition,
iPr_def_16 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_440,definition,
iPr_def_17 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_441,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_442,definition,
iPr_def_19 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_443,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_444,definition,
iPr_def_21 = multiply(sk_c3,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_445,definition,
iPr_def_22 = multiply(sk_c10,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_446,definition,
iPr_def_23 = multiply(sk_c1,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_447,definition,
iPr_def_24 = multiply(sk_c10,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_448,definition,
iPr_def_25 = inverse(sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_449,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_435,c_436]) ).
tcf(c_451,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c8) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_452,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_453,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c9) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_432]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_15 = sk_c10 )
| ( iPr_def_14 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_121,c_438,c_437]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_16 = sk_c10 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_120,c_439]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_119,c_440]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_118,c_441]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_117,c_442]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_20 = sk_c10 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_116,c_443]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_21 = sk_c4 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_115,c_444]) ).
tcf(c_461,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_114,c_445]) ).
tcf(c_462,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_14 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_113,c_446]) ).
tcf(c_467,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_20 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_468,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_21 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_469,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_475,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_20 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_476,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_21 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_477,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_478,negated_conjecture,
( ( iPr_def_14 = sk_c10 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_479,negated_conjecture,
( ( iPr_def_16 = sk_c10 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_483,negated_conjecture,
( ( iPr_def_20 = sk_c10 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_484,negated_conjecture,
( ( iPr_def_21 = sk_c4 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_485,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_486,negated_conjecture,
iPr_def_25 = sk_c9,
inference(demodulation,[status(thm)],[c_89,c_448]) ).
tcf(c_487,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_767,plain,
multiply(sk_c8,iPr_def_25) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_436,c_486]) ).
tcf(c_789,plain,
multiply(sk_c6,iPr_def_25) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_440,c_486]) ).
tcf(c_797,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_461,c_486]) ).
tcf(c_869,plain,
( ( sk_c10 = iPr_def_15 )
| ( multiply(iPr_def_20,sk_c4) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_459,c_445]) ).
tcf(c_895,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_15,sk_c2) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_797,c_447]) ).
tcf(c_898,plain,
( ( sk_c10 = iPr_def_14 )
| ( multiply(iPr_def_15,sk_c2) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_454,c_447]) ).
tcf(c_899,plain,
( ( sk_c10 = iPr_def_20 )
| ( multiply(sk_c10,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_467,c_447]) ).
tcf(c_922,plain,
multiply(iPr_def_25,sk_c10) = identity,
inference(superposition,[status(thm)],[c_448,c_87]) ).
tcf(c_923,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_443,c_87]) ).
tcf(c_926,plain,
multiply(iPr_def_15,sk_c1) = identity,
inference(superposition,[status(thm)],[c_438,c_87]) ).
tcf(c_927,plain,
! [X0: $i] :
( ( iPr_def_13 = sk_c10 )
| ( iPr_def_13 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_928,plain,
( ( iPr_def_13 = sk_c10 )
| ( iPr_def_13 != iPr_def_13 )
| ( sk_c10 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_927]) ).
tcf(c_929,plain,
iPr_def_13 = iPr_def_13,
inference(instantiation,[status(thm)],[c_487]) ).
tcf(c_950,plain,
( ( sk_c2 = iPr_def_23 )
| ( multiply(sk_c10,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_468,c_445]) ).
tcf(c_953,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c2 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_469,c_486]) ).
tcf(c_1148,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( sk_c10 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_475,c_486]) ).
tcf(c_1165,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( multiply(iPr_def_20,sk_c4) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1148,c_445]) ).
tcf(c_1212,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( sk_c4 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_476,c_486]) ).
tcf(c_1222,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_477,c_486]) ).
tcf(c_1271,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_25,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_478,c_922]) ).
tcf(c_1450,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_483,c_479]) ).
tcf(c_1451,plain,
( ( iPr_def_14 = iPr_def_20 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_483,c_478]) ).
tcf(c_1457,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_20,sk_c4) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_483,c_445]) ).
tcf(c_1522,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_485,c_486]) ).
tcf(c_1547,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_13) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1522,c_446]) ).
tcf(c_1617,plain,
( ~ iPr_def_12
| ( sk_c10 != iPr_def_14 )
| ( inverse(sk_c7) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_437,c_451]) ).
tcf(c_1629,plain,
( ~ iPr_def_12
| ( sk_c10 != iPr_def_16 )
| ( sk_c10 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_1617,c_439]) ).
tcf(c_1680,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_452,c_486]) ).
tcf(c_1701,plain,
( ~ iPr_def_11
| ( inverse(sk_c3) != sk_c10 )
| ( multiply(sk_c10,iPr_def_21) != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_444,c_1680]) ).
tcf(c_1702,plain,
( ~ iPr_def_11
| ( inverse(sk_c1) != sk_c10 )
| ( multiply(sk_c10,iPr_def_23) != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_446,c_1680]) ).
tcf(c_1727,plain,
( ~ iPr_def_11
| ( sk_c10 != iPr_def_20 )
| ( multiply(sk_c10,iPr_def_21) != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_1701,c_443]) ).
tcf(c_1879,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),iPr_def_25) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_453,c_486]) ).
tcf(c_1890,plain,
( ~ iPr_def_10
| ( multiply(sk_c10,iPr_def_25) != sk_c8 )
| ( multiply(inverse(sk_c10),iPr_def_25) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_448,c_1879]) ).
tcf(c_1892,plain,
( ~ iPr_def_10
| ( multiply(sk_c5,iPr_def_18) != sk_c8 )
| ( multiply(inverse(sk_c5),iPr_def_25) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_441,c_1879]) ).
tcf(c_1914,plain,
( ~ iPr_def_10
| ( multiply(iPr_def_25,iPr_def_25) != sk_c8 )
| ( multiply(sk_c10,iPr_def_25) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1890,c_448]) ).
tcf(c_2116,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_442,c_88]) ).
tcf(c_2117,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_437,c_88]) ).
tcf(c_2121,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_87,c_88]) ).
tcf(c_2123,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_25,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_767,c_88]) ).
tcf(c_2124,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_25,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_789,c_88]) ).
tcf(c_2125,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c10,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_922,c_88]) ).
tcf(c_2126,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_923,c_88]) ).
tcf(c_2129,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_926,c_88]) ).
tcf(c_2134,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2129,c_86]) ).
tcf(c_2137,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2126,c_86]) ).
tcf(c_2138,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c10,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2125,c_86]) ).
tcf(c_2763,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_13) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1450,c_446]) ).
tcf(c_2897,plain,
( ( iPr_def_14 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_13) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1451,c_446]) ).
tcf(c_3192,plain,
multiply(iPr_def_15,iPr_def_23) = sk_c10,
inference(superposition,[status(thm)],[c_446,c_2134]) ).
tcf(c_3195,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_23,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_3192,c_88]) ).
tcf(c_3268,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c10,
inference(superposition,[status(thm)],[c_444,c_2137]) ).
tcf(c_3497,plain,
multiply(iPr_def_25,iPr_def_22) = sk_c4,
inference(superposition,[status(thm)],[c_445,c_2138]) ).
tcf(c_3498,plain,
multiply(iPr_def_25,iPr_def_24) = sk_c2,
inference(superposition,[status(thm)],[c_447,c_2138]) ).
tcf(c_4031,plain,
( ( sk_c10 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_460,c_869]) ).
tcf(c_4033,plain,
( ( sk_c10 = iPr_def_22 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4031,c_3268]) ).
tcf(c_4147,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_15 )
| ( iPr_def_13 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_4033,c_449]) ).
tcf(c_5070,plain,
( ( sk_c10 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_462,c_898]) ).
tcf(c_7969,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_484,c_1457]) ).
tcf(c_7974,plain,
( ( sk_c10 = iPr_def_22 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_7969,c_3268]) ).
tcf(c_8066,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_7974,c_478]) ).
tcf(c_8070,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_25,iPr_def_22) = identity ) ),
inference(superposition,[status(thm)],[c_7974,c_922]) ).
tcf(c_8080,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_7974,c_449]) ).
tcf(c_8097,plain,
( ( sk_c4 = identity )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_8070,c_3497]) ).
tcf(c_8765,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c2 = iPr_def_23 )
| ( multiply(iPr_def_13,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8066,c_950]) ).
tcf(c_9244,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_15,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_953,c_895]) ).
tcf(c_9251,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_9244,c_3192]) ).
tcf(c_9337,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_9251,c_448]) ).
tcf(c_9995,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(sk_c10,identity) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8097,c_445]) ).
tcf(c_11008,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1212,c_1165]) ).
tcf(c_11012,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( sk_c10 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_11008,c_3268]) ).
tcf(c_11118,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( inverse(iPr_def_22) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_11012,c_448]) ).
tcf(c_12939,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_15,iPr_def_23) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1547,c_2134]) ).
tcf(c_14849,plain,
multiply(sk_c7,iPr_def_13) = multiply(iPr_def_14,iPr_def_25),
inference(superposition,[status(thm)],[c_767,c_2117]) ).
tcf(c_15755,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_4147,c_449,c_928,c_929,c_8080]) ).
tcf(c_15801,plain,
multiply(sk_c8,identity) = multiply(iPr_def_13,sk_c10),
inference(superposition,[status(thm)],[c_922,c_2123]) ).
tcf(c_16780,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2121,c_86]) ).
tcf(c_16818,plain,
multiply(inverse(sk_c3),iPr_def_21) = sk_c10,
inference(superposition,[status(thm)],[c_444,c_16780]) ).
tcf(c_16822,plain,
multiply(inverse(sk_c1),iPr_def_23) = sk_c10,
inference(superposition,[status(thm)],[c_446,c_16780]) ).
tcf(c_16824,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_87,c_16780]) ).
tcf(c_16937,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_2138,c_16780]) ).
tcf(c_16942,plain,
multiply(inverse(iPr_def_15),sk_c10) = iPr_def_23,
inference(superposition,[status(thm)],[c_3192,c_16780]) ).
tcf(c_16962,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,iPr_def_25)) = iPr_def_13,
inference(superposition,[status(thm)],[c_14849,c_16780]) ).
tcf(c_16966,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_16780,c_16780]) ).
tcf(c_17830,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_16824,c_16966]) ).
tcf(c_17831,plain,
multiply(iPr_def_13,sk_c10) = sk_c8,
inference(demodulation,[status(thm)],[c_15801,c_17830]) ).
tcf(c_17847,plain,
multiply(sk_c5,sk_c6) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_17830,c_2116]) ).
tcf(c_17850,plain,
multiply(sk_c6,iPr_def_25) = multiply(iPr_def_17,identity),
inference(superposition,[status(thm)],[c_17830,c_2124]) ).
tcf(c_17863,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_17850,c_789]) ).
tcf(c_17865,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_17847,c_442]) ).
tcf(c_18035,plain,
multiply(inverse(iPr_def_13),sk_c8) = sk_c10,
inference(superposition,[status(thm)],[c_17831,c_16780]) ).
tcf(c_19552,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_13)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_18035,c_451]) ).
tcf(c_21764,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_15,iPr_def_23) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_2134]) ).
tcf(c_21783,plain,
multiply(sk_c10,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_16937,c_87]) ).
tcf(c_21787,plain,
! [X0: $i] : multiply(sk_c10,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_16937,c_16780]) ).
tcf(c_21788,plain,
multiply(sk_c10,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_16937,c_17830]) ).
tcf(c_22478,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_25) = identity ) ),
inference(superposition,[status(thm)],[c_478,c_21783]) ).
tcf(c_22983,plain,
inverse(iPr_def_25) = sk_c10,
inference(demodulation,[status(thm)],[c_21788,c_17830]) ).
tcf(c_22995,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_24) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_1222,c_22983]) ).
tcf(c_23123,plain,
multiply(sk_c10,identity) = sk_c10,
inference(superposition,[status(thm)],[c_922,c_21787]) ).
tcf(c_23135,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(sk_c10,identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1271,c_21787]) ).
tcf(c_23137,plain,
multiply(sk_c10,sk_c4) = iPr_def_22,
inference(superposition,[status(thm)],[c_3497,c_21787]) ).
tcf(c_24205,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_22995,c_9337]) ).
tcf(c_24219,plain,
( ( iPr_def_14 = iPr_def_20 )
| ( multiply(iPr_def_15,iPr_def_23) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2897,c_2134]) ).
tcf(c_25039,plain,
multiply(sk_c10,identity) = multiply(iPr_def_15,iPr_def_23),
inference(superposition,[status(thm)],[c_17830,c_3195]) ).
tcf(c_25344,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_13 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_24205,c_1522]) ).
tcf(c_25690,plain,
( ( iPr_def_13 = iPr_def_25 )
| ( inverse(iPr_def_22) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_25344,c_22983]) ).
tcf(c_25724,plain,
( ( iPr_def_13 = iPr_def_25 )
| ( multiply(iPr_def_22,iPr_def_22) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_25344,c_3497]) ).
tcf(c_26479,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_25724,c_25690,c_25344,c_25039,c_24219,c_23137,c_23135,c_23123,c_22983,c_22478,c_21783,c_21764,c_19552,c_17865,c_17863,c_17850,c_17847,c_17831,c_16962,c_16942,c_16822,c_16818,c_15755,c_12939,c_11118,c_9995,c_8765,c_5070,c_3498,c_1914,c_1892,c_1727,c_1702,c_1629,c_922,c_899,c_486,c_461,c_460,c_459,c_458,c_457,c_456,c_455,c_454,c_449,c_448,c_443,c_441,c_439,c_438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP388-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Wed Sep 23 14:38:36 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.33 Running first-order theorem proving
% 0.02/0.33 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.34
% 0.02/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.34
% 0.02/0.34 % Detected problem language: tptp
% 0.09/0.35 % Proving...
% 4.57/2.09 % SZS status Started for theBenchmark.p
% 4.57/2.09 % SZS status Unsatisfiable for theBenchmark.p
% 4.57/2.09
% 4.57/2.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.57/2.09
% 4.57/2.09 % ------ iProver source info
% 4.57/2.09
% 4.57/2.09 % git: date: 2026-07-19 20:42:38 +0200
% 4.57/2.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.57/2.09 % git: non_committed_changes: false
% 4.57/2.09
% 4.57/2.09 % ------ Parsing...% successful
% 4.57/2.09
% 4.57/2.09
% 4.57/2.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.57/2.09
% 4.57/2.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.57/2.09
% 4.57/2.09 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.57/2.09
% 4.57/2.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.57/2.09 % ------ Proving...
% 4.57/2.09 % ------ Problem Properties
% 4.57/2.09
% 4.57/2.09 %
% 4.57/2.09 % clauses 53
% 4.57/2.09 % conjectures 37
% 4.57/2.09 % EPR 34
% 4.57/2.09 % Horn 20
% 4.57/2.09 % unary 17
% 4.57/2.09 % binary 32
% 4.57/2.09 % lits 94
% 4.57/2.09 % lits eq 88
% 4.57/2.09 % fd_pure 0
% 4.57/2.09 % fd_pseudo 0
% 4.57/2.09 % fd_cond 0
% 4.57/2.09 % fd_pseudo_cond 0
% 4.57/2.09 % AC symbols 0
% 4.57/2.09
% 4.57/2.09 % ------ Schedule dynamic 5 is on
% 4.57/2.09
% 4.57/2.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.57/2.09
% 4.57/2.09
% 4.57/2.09 % ------
% 4.57/2.09 % Current options:
% 4.57/2.09 % ------
% 4.57/2.09
% 4.57/2.09
% 4.57/2.09 %
% 4.57/2.09
% 4.57/2.09 % ------ Proving...
% 4.57/2.09 %
% 4.57/2.09
% 4.57/2.09 % SZS status Unsatisfiable for theBenchmark.p
% 4.57/2.09
% 4.57/2.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.57/2.09
% 4.57/2.09
%------------------------------------------------------------------------------